For Part (a), differentiate the position function twice
Differentiate once to get the velocity and again to get the acceleration as follows,
For Part (b), see what values of
make the velocity negative
0 to get
The object is moving to the left when
is in the interval (0,3/2).
For Part (c), see what values of
make the velocity zero
= 0 and solve, as follows
– 3 = 0
Thus, the object is stationary when
Find the position of the particle at this time
= 3/2 as follows
For Part (d), find the velocity when
= 1 and 2
= 2(1) – 3 = –1.
= 2(2) – 3 = 1.
Take the absolute value of velocity to get speed
The speed when the particle is at the origin is 1 in both cases when
= 1 and
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